I'm "living the dream" as a Plebe at USNA. If your GPA is as good as you say it is, and you've taken challenging classes, as well as have some participation in sports and/or other examples of leadership, you would probably be competitive.
They do use the SAT. They say above 1800 is the baseline, but you'd want to be higher than that, I was at a 2010.
If you decide to go the academy route, you need to start applying in February of your Junior year, and DON'T get discouraged by the application process, because it is many times longer than the application for any other type of college. Good luck, keep up the hard work.
Roger that Brother, thanks for setting me up for success. I wouldn't be around now if guys like you hadn't passed on their knowledge.